Plane coordinates and distance

Find distances, midpoints, and internal division points using coordinates and check geometric meaning.

Meaning

Coordinates express distances and positions dividing a segment numerically. Plane distance is the hypotenuse of the right triangle formed by horizontal and vertical differences.

Example

The distance between and is Their midpoint is The midpoint makes half the horizontal and half the vertical displacement. Adding half the difference to the starting coordinate gives 1+(4−1)/2=(1+4)/2, explaining the coordinate averages.Coordinate differences can be signed, but distance is nonnegative. Check that units and axis scales define the same distance system.

Practice for this concept

Scope and references

Topics

Distance between points, midpoints, internal division of segments

Learning goal

Find distances, midpoints, and internal division points using coordinates and check geometric meaning.

Helpful background

Connect coordinate differences, the Pythagorean theorem, and ratios.